Logic and Completeness

The course is included in the degree programme H2LOG Logic, Master's programme and can also be given as a freestanding course.

Admission to the course requires successful completion of

• at least 60 credits in total in the subject areas mathematics, logic, computer scienceor formal linguistics, or
• at least 90 credits in philosophy or linguistics, and at least 30 credits in total in the subject areas mathematics, logic, computer science or formal linguistics,

or equivalent knowledge. English 6 or equivalent is also required.

Formal logic is the study of reasoning and meaning from a rigourous and mathematically precise standpoint. This course provides an introduction to formal logic central to the fields of mathematics, philosophy and theoretical computer science. The course covers two formal logics in detail, propositional logic and first order predicate logic, giving a comprehensive overview of their syntax, semantics and proof systems. Detailed proofs of the soundness and completeness theorems for both propositional and predicate logic are included. Elementary results on the semantics of predicate logic, such as the compactness theorem and (downwards) Löwenheim–Skolem–Tarski theorem, are presented with applications.

On successful completion of the course the student will be able to:

Knowledge and understanding

• demonstrate knowledge of the syntax and semantics of propositional and predicate logic,
• demonstrate an understanding of the central results from the course, including soundness and completeness for propositional and predicate logic,
• present formal derivations for propositional and predicate logic in a proof system such as natural deduction,

Competence and skills

• relate syntactic concepts, such as substitution and derivability, to semantic phenomena and vice versa,
• formulate and present proofs of the central results in the course and their dependent lemmas,
• apply methods and results from the course in independent problem-solving,

Judgement and approach

• critically assess the applicability of formal logic in modelling phenomena.

Teaching is given in the form of lectures, seminars, exercises, individual assignments and group assignments.

Language of instruction: English

The course is assessed individually in written form. In addition to written final examination, there may also be up to four compulsory homework assignments during the course.

The grading teacher may request completion of examined student achievements.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The course is given one of the grades Pass with distinction (VG), Pass (G) and Fail (U). All compulsory elements of the course must be completed to obtain a passing grade. To receive a Pass with distinction, it is furthermore required that the written exam receives the assessment Pass with distinction.

Students who participate in or have completed the course are given the opportunity to anonymously express their experiences of and views on it in a course evaluation. A compilation of the course evaluation and the reflection of the teacher responsible for the course is made available to the students within a reasonable time after the end of the course. The next time the course is given, the summary and any implemented measures will be presented.

The course requires access to a computer (or equivalent) with internet connection.
The course may not be included in the degree together with the course LOG110 or LOG111.